Question

Carry out the following arithmetic operations. (Enter your answers to the correct number of significant figures.) My Notes Ask Your (a) the sum of the measured values 521, 31.4, 0.85, and 9.0 (b) the product 0.0052 x 386.2 (c) the product 15.70 x π

Answer 1

Answer :

(a) The answer will be $\Rightarrow 562$

(b) The answer will be $\Rightarrow 2.0$

(c) The answer will be $\Rightarrow 49.32$

Explanation :

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

The rule apply for the multiplication and division is :

The least number of significant figures in any number of the problem determines the number of significant figures in the answer.

The rule apply for the addition and subtraction is :

The least precise number present after the decimal point determines the number of significant figures in the answer.

(a) The sum of the measured values 521, 31.4, 0.85, and 9.0

$521+31.4+0.85+9.0$

$\Rightarrow 562.25$

In the given expression, 521 has 3 significant figures, 31.4 has 3 significant figures, 0.85 has 2 significant figures and 9.0 has 2 significant figures. From this we conclude that least precise number present after the decimal point is 0.

Thus, the answer will be $\Rightarrow 562$

(b) The product 0.0052 × 386.2

$(0.0052)\times (386.2)$

$\Rightarrow 2.00824$

In the given expression, 0.0052 has 2 significant figures and 386.2 has 4 significant figures. From this we conclude that 2 is the least significant figures in this problem. So, the answer should be in 2 significant figures.

Thus, the answer will be $\Rightarrow 2.0$

(c) The product $15.70\times \pi$

The value of $\pi$ = 3.141414 = $3.\bar {14}$

$\pi$ is an irrational number.

$(15.70)\times (3.1414)$

$\Rightarrow 49.31998$

In the given expression, 15.70 has 4 significant figures and $3.\bar {14}$ has infinite significant figures. From this we conclude that 4 is the least significant figures in this problem. So, the answer should be in 4 significant figures.

Thus, the answer will be $\Rightarrow 49.32$